Mistuning-Based Control Design to Improve Closed-Loop Stability Margin of Vehicular Platoons
TLDR
It is proved that with arbitrary small amounts of mistuning, the asymptotic behavior of the least stable closed loop eigenvalue can be improved to O(1/N) in the limit of a large number of vehicles.Abstract:
We consider a decentralized bidirectional control of a platoon of N identical vehicles moving in a straight line. The control objective is for each vehicle to maintain a constant velocity and inter-vehicular separation using only the local information from itself and its two nearest neighbors. Each vehicle is modeled as a double integrator. To aid the analysis, we use continuous approximation to derive a partial differential equation (PDE) approximation of the discrete platoon dynamics. The PDE model is used to explain the progressive loss of closed-loop stability with increasing number of vehicles, and to devise ways to combat this loss of stability. If every vehicle uses the same controller, we show that the least stable closed-loop eigenvalue approaches zero as O(1/N2) in the limit of a large number (N) of vehicles. We then show how to ameliorate this loss of stability by small amounts of "mistuning", i.e., changing the controller gains from their nominal values. We prove that with arbitrary small amounts of mistuning, the asymptotic behavior of the least stable closed loop eigenvalue can be improved to O(1/N). All the conclusions drawn from analysis of the PDE model are corroborated via numerical calculations of the state-space platoon model.read more
Citations
More filters
Journal ArticleDOI
Control of Leader-Following Vehicle Platoons With Varied Communication Range
Shixi Wen,Ge Guo +1 more
TL;DR: This article investigates the control problem for leader-following vehicle platoons with a constant-spacing policy, where the information of the leader is broadcast to each follower via vehicular ad hoc networks (VANETs) subject to varied communication ranges.
Proceedings ArticleDOI
Effect of network structure on the stability margin of large vehicle formation with distributed control
TL;DR: The problem of distributed control of a large network of double-integrator agents to maintain a rigid formation is studied, and the stability margin of the closed loop is measured by the real part of the least stable eigenvalue of the state matrix.
Proceedings ArticleDOI
Control of large 1D networks of double integrator agents: Role of heterogeneity and asymmetry on stability margin
He Hao,Prabir Barooah +1 more
TL;DR: This work considers the distributed control of a network of heterogeneous agents with double integrator dynamics to maintain a rigid formation in 1D and shows that heterogeneity has little effect while asymmetry has a significant effect on the stability margin.
Journal ArticleDOI
Transients of platoons with asymmetric and different Laplacians
TL;DR: It is shown that the parameters can be chosen so that the platoon behaves as a wave equation with different wave velocities, and suggests that the system has a better performance than other nearest-neighbor scenarios.
Journal ArticleDOI
The joint network/control design of platooning algorithms can enforce guaranteed safety constraints
TL;DR: This work designs a cooperative driving system from a joint network and control perspective, determining upper bounds on the error subject to packet losses in the network, so that the actual inter-vehicle gap can be tuned depending on vehicle or network performance.
References
More filters
Book
Semigroups of Linear Operators and Applications to Partial Differential Equations
TL;DR: In this article, the authors considered the generation and representation of a generator of C0-Semigroups of Bounded Linear Operators and derived the following properties: 1.1 Generation and Representation.
Book
Spectral Methods in Fluid Dynamics
M. Y. Hussaini,Thomas A. Zang +1 more
TL;DR: Spectral methods have been widely used in simulation of stability, transition, and turbulence as discussed by the authors, and their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed.
Journal Article
On kinetic waves, II . A theory of traffic flow on long crowded roads
M J Lighthill,G B Whitham +1 more
TL;DR: In this paper, a functional relationship between flow and concentration for traffic on crowded arterial roads has been postulated for some time, and has experimental backing, from which a theory of the propagation of changes in traffic distribution along these roads may be deduced.
Journal ArticleDOI
On kinematic waves II. A theory of traffic flow on long crowded roads
TL;DR: The theory of kinematic waves is applied to the problem of estimating how a ‘hump’, or region of increased concentration, will move along a crowded main road, and is applicable principally to traffic behaviour over a long stretch of road.
Journal ArticleDOI
Traffic and related self-driven many-particle systems
Dirk Helbing,Dirk Helbing +1 more
TL;DR: This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic, including microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models.